Equation based state estimate for air system controller

ABSTRACT

A system for providing oxygen to a fuel cell circuit includes a compressor and a fuel cell stack having a plurality of fuel cells. The system also includes a plurality of pipes and a pressure sensor designed to detect pressure at a first location. The system also includes a memory to store a model of the fuel cell circuit and an ECU. The ECU determines a control signal corresponding to desirable operation of the compressor and determines flow values of the gas through each component based on the detected pressure and the model of the fuel cell circuit. The ECU also determines pressure values of each component based on the determined flow values and the model of the fuel cell circuit. The ECU also controls operation of the compressor based on the control signal, at least one of the flow values, and at least one of the pressure values.

BACKGROUND 1. Field

The present disclosure relates to systems and methods for controllingpressure and airflow values of air flowing through a fuel cell circuitby estimating the pressure and airflow values, identifying a desirablepath for the pressure and airflow values, and feedforward and feedbackcontrol of actuators to achieve the desirable path of the pressure andairflow values.

2. Description of the Related Art

Due to a combination of state and federal regulations, along with adesire to reduce pollution, there has been a recent push for vehiclemanufacturers to design fuel-efficient vehicles that have relatively lowlevels of harmful emissions. Automobile manufacturers have discoveredmultiple solutions to reducing these harmful emissions. One suchsolution is hybrid vehicles that include an engine, as well as a batteryfor storing energy and a motor-generator for powering the vehicle usingthe electricity. Another solution is fully electronic vehicles thatinclude only a battery and a motor-generator that powers the vehicleusing energy stored in the battery. Yet another solution is fuel cellvehicles that include fuel cells that generate electricity via achemical reaction.

Many fuel cell vehicles include one or more fuel cell stack thatincludes multiple fuel cells. The fuel cells may receive a fuel, whichtypically includes hydrogen, along with oxygen or another oxidizingagent. The fuel cell stack may facilitate a chemical reaction betweenthe hydrogen and oxygen. This chemical reaction generates electricity.The main emissions are air and water, which are relatively harmless. Theelectricity generated by the fuel cell stack may be stored in a batteryor directly provided to a motor-generator to generate mechanical powerto propel the vehicle. While fuel cell vehicles are an exciting advancein the automobile industry, the technology is relatively new, providingspace for improvements to the technology.

Many fuel cells receive the oxygen from air. However, the amount ofoxygen (i.e., air) required varies based on a desired power output ofthe fuel cells. The pressure of the air within the fuel cells likewisevaries based on the desired power output of the fuel cells. The desiredpower output is variable and is based on a power request from a driver,or an electronic control unit if the vehicle is an autonomous orsemi-autonomous vehicle.

Thus, there is a need in the art for systems and methods for accuratelyand quickly providing air at a desirable rate and a desirable pressureto the fuel cells.

SUMMARY

Described herein is a system for providing oxygen to a fuel cellcircuit. The system includes a compressor designed to pump a gas throughthe fuel cell circuit. The system further includes a fuel cell stackhaving a plurality of fuel cells and designed to receive the gas. Thesystem also includes a plurality of pipes each designed to transport thegas throughout a portion of the fuel cell stack. The system alsoincludes a pressure sensor designed to detect a detected pressure of thegas at a first location of the fuel cell circuit. The system alsoincludes a memory designed to store a model of the fuel cell circuit.The system also includes an electronic control unit (ECU) coupled to thecompressor, the pressure sensor, and the memory. The ECU is designed todetermine or receive a control signal corresponding to desirableoperation of the compressor. The ECU is further designed to determineflow values of the gas through each of the compressor, the fuel cellstack, and the plurality of pipes based on the detected pressure and themodel of the fuel cell circuit. The ECU is further designed to determinepressure values at each of the compressor, the fuel cell stack, and theplurality of pipes based on the determined flow values and the model ofthe fuel cell circuit. The ECU is further designed to control operationof the compressor based on the control signal, at least one of the flowvalues, and at least one of the pressure values.

Also described is a system for providing oxygen to a fuel cell circuit.The system includes a fuel cell stack having a plurality of fuel cellsand designed to receive a gas. The system also includes a bypass branchdesigned to cause at least some of the gas to bypass the fuel cellstack. The system also includes a bypass valve having a bypass valveposition and designed to adjust an amount of the gas that bypasses thefuel cell stack. The system also includes a flow sensor designed todetect a detected flow of the gas flowing through a first location ofthe fuel cell circuit. The system also includes a memory designed tostore a model of the fuel cell circuit. The system also includes anelectronic control unit (ECU) coupled to the bypass valve, the flowsensor, and the memory. The ECU is designed to determine or receive acontrol signal corresponding to desirable operation of the bypass valve.The ECU is also designed to determine flow values of the gas througheach of the bypass branch and the fuel cell stack based on the detectedflow and the model of the fuel cell circuit, the flow values including acurrent bypass flow value corresponding to flow through the bypassbranch, the current bypass flow value being determined based on thebypass valve position and a previous bypass pressure value correspondingto the bypass branch that was determined during a previous timestep. TheECU is also designed to determine pressure values at each of the bypassbranch and the fuel cell stack based on the determined flow values andthe model of the fuel cell circuit. The ECU is also designed to controloperation of the bypass valve based on the control signal, at least oneof the flow values, and at least one of the pressure values.

Also described is a method for providing oxygen to fuel cells. Themethod includes storing, in a memory, a model of a fuel cell circuithaving multiple components including a compressor and a fuel cell stack.The method also includes receiving, from a flow sensor, a detected massflow of a gas flowing through a first location of the fuel cell circuit.The method also includes determining, by the ECU, mass flow valuescorresponding to mass flow of the gas through each of the multiplecomponents of the fuel cell circuit. The method also includesdetermining, by the ECU, a Reynolds number for each of the multiplecomponents based on the mass flow values. The method also includesdetermining, by the ECU, whether flow of the gas through each of themultiple components of the fuel cell circuit is a laminar flow, aturbulent flow, or a mixed flow based on the Reynolds number. The methodalso includes determining, by the ECU, laminar, turbulent, or mixed flowvalues of the gas based on the mass flow values and whether the flow ofthe gas through each of the multiple components is the laminar flow, theturbulent flow, or the mixed flow. The method also includes determining,by the ECU, pressure values for each of the multiple components of thefuel cell circuit based on the laminar, turbulent, or mixed flow values.The method also includes controlling, by the ECU, operation of thecompressor based on at least one of the laminar, turbulent, or mixedflow values and at least one of the pressure values.

BRIEF DESCRIPTION OF THE DRAWINGS

Other systems, methods, features, and advantages of the presentinvention will be or will become apparent to one of ordinary skill inthe art upon examination of the following figures and detaileddescription. It is intended that all such additional systems, methods,features, and advantages be included within this description, be withinthe scope of the present invention, and be protected by the accompanyingclaims. Component parts shown in the drawings are not necessarily toscale, and may be exaggerated to better illustrate the importantfeatures of the present invention. In the drawings, like referencenumerals designate like parts throughout the different views, wherein:

FIG. 1 is a block diagram illustrating various components of a vehiclehaving a fuel cell circuit capable of generating electricity based on achemical reaction according to an embodiment of the present invention;

FIG. 2 is a block diagram illustrating various features of the fuel cellcircuit of FIG. 1 according to an embodiment of the present invention;

FIG. 3 is cross-sectional view of an exemplary compressor for use in afuel cell circuit according to an embodiment of the present invention;

FIG. 4 is a block diagram illustrating various logic components of anelectronic control unit (ECU) of the vehicle of FIG. 1 for providing agas to the fuel cell circuit at a desirable flow rate and pressureaccording to an embodiment of the present invention;

FIGS. 5A and 5B are flowcharts illustrating a method for estimatingpressure and flow values for multiple components of a fuel cell circuitaccording to an embodiment of the present invention;

FIGS. 6A and 6B are flowcharts illustrating a method for determining adesirable progression, or path, of multiple parameters of a fuel cellcircuit according to an embodiment of the present invention;

FIG. 7 is speed map that plots airflow rates and pressure ratios withcorresponding compressor speeds of a compressor used in a fuel cellcircuit according to an embodiment of the present invention;

FIG. 8 illustrates stored compressor flow maps along with aninterpolated compressor flow map interpolated using the storedcompressor flow maps according to an embodiment of the presentinvention;

FIG. 9 illustrates the interpolated compressor flow map of FIG. 8 alongwith a fuel cell flow rate map and a compressor pressure ratio map thatfollow the progression of the compressor flow map according to anembodiment of the present invention;

FIG. 10 includes various maps and graphs that illustrate a progressionalong the interpolated compressor flow map and the compressor pressureratio map of FIG. 9 from an initial request until a target has beenreached according to an embodiment of the present invention;

FIG. 11 is a flowchart illustrating a method for a feedforward controlof a valve of a fuel cell circuit according to an embodiment of thepresent invention;

FIG. 12 illustrates an exemplary valve for use in a fuel cell circuitaccording to an embodiment of the present invention;

FIGS. 13A and 13B are flowcharts illustrating a method for feedforwardcontrol of a compressor of a fuel cell circuit according to anembodiment of the present invention;

FIG. 14 is a block diagram illustrating a control circuit forimplementing the method of FIGS. 13A and 13B according to an embodimentof the present invention;

FIGS. 15A and 15B are flowcharts illustrating a method for feedbackcontrol of a valve of a fuel cell circuit according to an embodiment ofthe present invention;

FIGS. 16A and 16B illustrate pressure maps used in the method of FIGS.15A and 15B according to an embodiment of the present invention;

FIGS. 17A and 17B are block diagrams illustrating control circuits forimplementing the method of FIGS. 16A and 16B according to an embodimentof the present invention;

FIGS. 18A and 18B are flowcharts illustrating a method for feedbackcontrol of a compressor of a fuel cell circuit according to anembodiment of the present invention;

FIG. 19 is an airflow map used in the method of FIGS. 18A and 18Baccording to an embodiment of the present invention; and

FIGS. 20A and 20B are block diagrams illustrating control circuits forimplementing the method of FIGS. 18A and 18B according to an embodimentof the present invention.

DETAILED DESCRIPTION

The present disclosure describes systems and methods for providing airto a fuel cell circuit. The systems provide several benefits andadvantages such as estimating airflow and pressure values for eachcomponent of the fuel cell circuit. The estimations are based on datadetected by a single airflow sensor and a single pressure sensor yetadvantageously provide relatively accurate estimation of the values. Thefuel cell circuit includes only two sensors, thus beneficially reducinga cost of the fuel cell circuit due to the relatively few sensors thatare included. The system estimates the flow and pressure values for eachcomponent during each timestep, advantageously providing other controlsystems with near real-time information.

An exemplary system includes a compressor to pump gas through a fuelcell circuit, where it may be received by a fuel cell stack thatincludes multiple fuel cells. The system further includes a plurality ofpipes for transporting the gas and a pressure sensor designed to detecta pressure of the gas. The system includes a memory that stores a modelof the fuel cell circuit, along with an electronic control unit (ECU).The ECU may calculate flow and pressure values of the gas throughout thefuel cell circuit based on the pressure detected by the pressure sensor.The ECU can then control the compressor based on a received controlsignal and the calculated flow and pressure values.

Turning to FIG. 1, a vehicle 100 includes components of a system 101 forproviding gas, such as air, to fuel cells. In particular, the vehicle100 and system 101 include an ECU 102 and a memory 104. The vehicle 100further includes a power source 110 which may include at least one of anengine 112, a motor-generator 114, a battery 116, or a fuel cell circuit118. The fuel cell circuit 118 may be a part of the system 101.

The ECU 102 may be coupled to each of the components of the vehicle 100and may include one or more processors or controllers, which may bespecifically designed for automotive systems. The functions of the ECU102 may be implemented in a single ECU or in multiple ECUs. The ECU 102may receive data from components of the vehicle 100, may makedeterminations based on the received data, and may control the operationof components based on the determinations.

In some embodiments, the vehicle 100 may be fully autonomous orsemi-autonomous. In that regard, the ECU 102 may control various aspectsof the vehicle 100 (such as steering, braking, accelerating, or thelike) to maneuver the vehicle 100 from a starting location to adestination.

The memory 104 may include any non-transitory memory known in the art.In that regard, the memory 104 may store machine-readable instructionsusable by the ECU 102 and may store other data as requested by the ECU102 or programmed by a vehicle manufacturer or operator. The memory 104may store a model of the fuel cell circuit 118. The model may includeequations or other information usable to estimate various parameters ofthe fuel cell circuit 118.

The engine 112 may convert a fuel into mechanical power. In that regard,the engine 112 may be a gasoline engine, a diesel engine, or the like.

The battery 116 may store electrical energy. In some embodiments, thebattery 116 may include any one or more energy storage device includinga battery, a fly-wheel, a super-capacitor, a thermal storage device, orthe like.

The fuel cell circuit 118 may include a plurality of fuel cells thatfacilitate a chemical reaction to generate electrical energy. Forexample, the fuel cells may receive hydrogen and oxygen, facilitate areaction between the hydrogen and oxygen, and output electricity inresponse to the reaction. In that regard, the electrical energygenerated by the fuel cell circuit 118 may be stored in the battery 116.In some embodiments, the vehicle 100 may include multiple fuel cellcircuits including the fuel cell circuit 118.

The motor-generator 114 may convert the electrical energy stored in thebattery (or electrical energy received directly from the fuel cellcircuit 118) into mechanical power usable to propel the vehicle 100. Themotor-generator 114 may further convert mechanical power received fromthe engine 112 or wheels of the vehicle 100 into electricity, which maybe stored in the battery 116 as energy and/or used by other componentsof the vehicle 100. In some embodiments, the motor-generator 114 mayalso or instead include a turbine or other device capable of generatingthrust.

Turning now to FIG. 2, additional details of the fuel cell circuit 118are illustrated. In particular, the fuel cell circuit 118 includes anair intake 200, an air cleaner 202, a compressor 204, an intercooler206, a fuel cell stack 208, a bypass branch 210, a bypass valve 212positioned along the bypass branch 210, and a restriction valve 214.

The air intake 200 may receive air from an ambient environment, such asoutside of the vehicle 100 of FIG. 1. In some embodiments, the airintake 200 may include a filter for filtering debris from the receivedair. The air cleaner 202 may include a filter or other device capable ofremoving debris and other impurities from the air received from the airintake 200.

The compressor 204 may be a turbo compressor or other compressor capableof pressurizing air. In that regard, the compressor 204 may draw airfrom the cleaner 202 and may output pressurized air.

With brief reference to FIG. 3, an exemplary compressor 300 may be usedas the compressor 204 of FIG. 2. In particular, the compressor 300includes a body 302 through which air may be drawn. An impeller 304,which may include a plurality of airfoils, may be located inside of thebody 302. A motor 306 (or other torque source) may generate mechanicalpower having a torque at a rotational speed, which may be received by agearbox 308 via a shaft 310. The gearbox 308 may convert the powerreceived from the motor 306 into power having a different torque androtational speed. The mechanical power from the gearbox 308 may beapplied to the impeller 304 via the shaft 312. The pressure of the gasoutput by the compressor 300 may be dependent upon the torque and speedof the mechanical power applied to the impeller 304.

Returning reference to FIG. 2, the fuel cell circuit 118 may furtherinclude an intercooler 206. The intercooler 206 may receive the air fromthe compressor 204 and may also receive a fluid, such as a coolant. Theintercooler 206 may transfer heat from the air to the coolant, or maytransfer heat from the coolant to the air. In that regard, theintercooler 206 may adjust a temperature of the air flowing through thefuel cell circuit 118.

The fuel cell stack 208 may include a plurality of fuel cells. The fuelcells may receive hydrogen along with the air from the intercooler 206.The fuel cells may facilitate a chemical reaction between the oxygen inthe air and the hydrogen, which may generate electricity.

The air from the intercooler 206 may be split such that some of the airflows through the fuel cell stack 208 and some of the air flows throughthe bypass branch 210. In that regard, the air flowing through thebypass branch 210 fails to flow through the fuel cell stack 208. Thebypass valve 212 may have an adjustable valve position. The adjustablevalve position of the bypass valve 212 may be controlled to adjust anamount of airflow through the bypass branch 210 and, likewise, to adjustan amount of airflow through the fuel cell stack 208. For example, whenthe bypass valve 212 is 100 percent (100%) closed then all of theairflow through the fuel cell circuit 118 flows through the fuel cellstack 208.

Although discussion may reference airflow through the fuel cell circuit118, one skilled in the art will realize that any other gas flow may besubstituted for the airflow without departing from the scope of thepresent disclosure.

The restriction valve 214 may likewise have an adjustable valveposition. The adjustable valve position of the restriction valve 214 maybe controlled to adjust a pressure of the air within the fuel cell stack208. For example, the pressure within the fuel cell stack 208 may beincreased by closing the restriction valve 214, and may be decreased byopening the restriction valve 214.

Referring to FIGS. 1 and 2, each of the compressor 204, the bypass valve212, and the restriction valve 214 may be considered actuators and maybe controlled by the ECU 102. For example, the ECU 102 may receive apower request from a driver of the vehicle (or may generate a powerrequest in an autonomous or semi-autonomous vehicle). The ECU 102 mayconvert the power request into desirable pressure or flow valuescorresponding to desirable pressure or airflow at specific locationswithin the fuel cell circuit 118. The ECU 102 may then control each ofthe compressor 204, the bypass valve 212, and the restriction valve 214in order to achieve the desirable pressure or flow values.

The fuel cell circuit 118 may further include a flow sensor 216 and apressure sensor 218. The flow sensor 216 may detect a flow of the gas(such as a mass flow) through the compressor 204. The pressure sensor218 may detect a pressure of the gas at an outlet of the intercooler206.

The fuel cell circuit 118 may further include a plurality of pipes 220.For example, the plurality of pipes 220 may include a first pipe 222that transfers the gas from the intake 200 to the air cleaner 202, and asecond pipe 224 that transfers the gas from the air cleaner 202 to theflow sensor 216. In some embodiments, two or more of the intake 200, theair cleaner 202, or the flow sensor 216 may be directly connectedwithout any pipes.

Referring now to FIGS. 2 and 4, the ECU 102 may include variousprocesses or functions for controlling the fuel cell circuit 118. Theprocesses or functions within the ECU 102 may each be implemented inhardware (i.e., performed by a dedicated hardware), may be implementedin software (i.e., a general purpose ECU running software stored in amemory), or may be implemented via a combination of hardware andsoftware.

In particular, the ECU 102 may include a state mediator 400. The statemediator 400 may receive a control signal 402 corresponding to desirablepressure and/or flow values (i.e., at least one target pressure value orat least one target flow value). The control signal 402 may likewisecorrespond to a power request. The state mediator 400 may analyze thetarget pressure and flow values and determine whether the target valuesare feasible based on the mechanics of the fuel cell circuit 118 andwhether one or more component of the fuel cell circuit 118 is likely tobecome damaged in an attempt to meet a target value. The state mediator400 may then output mediated target values 404.

The ECU 102 may further include a state estimator 406. The stateestimator 406 may receive the mediated target values 404 along withsensor data 408 detected by the flow sensor 216 and the pressure sensor218. The state estimator 406 may calculate or estimate current pressurevalues and flow values corresponding to each component of the fuel cellcircuit 118 (including the plurality of pipes 220). The state estimator406 may output the current estimated values 410. In some embodiments,the state estimator 406 may also determine or adjust the mediated targetvalues 404.

The ECU 102 may also include a path controller 412. The path controller412 may receive the current estimated values 410 along with the mediatedtarget values 404. The path controller 412 may identify a desirable pathfrom the current estimated values 410 to the mediated target values 404.The path controller 412 may determine and output desirable intermediatetargets 414 that lay along the desirable path from the current estimatedvalues 410 to the mediated target values 404.

The ECU 102 may also include a feedforward and feedback control 416. Thefeedforward and feedback control 416 may receive the desirableintermediate targets 414 along with the current estimated values 410.The feedforward and feedback control 416 may determine and outputcontrol signals 418 that may control operation of the actuators of thefuel cell circuit 118.

Referring now to FIGS. 2, 4, 5A, and 5B, a method 500 for estimating thecurrent estimated values 410 may be performed by components of thesystem 101, such as by the state estimator 406. In block 502, the ECU102 may determine or receive a control signal, such as the mediatedtarget values 404, corresponding to desirable operation of theactuators. For example, the control signal may include or correspond totarget pressure and flow values at various locations throughout the fuelcell circuit 118. As described above, the compressor 204, bypass valve212, and restriction valve 214 may be controlled to adjust the pressureand flow values throughout the fuel cell circuit 118.

In block 504, the flow sensor 216 and the pressure sensor 218 may detecta current mass flow value of the gas flowing through the compressor 204and a current pressure value corresponding to pressure of the gas at theoutlet of the intercooler 206.

In block 506, the ECU 102 may calculate mass flow values of the gasthrough the components of the fuel cell circuit based on thecharacteristics of the components, settings of the actuators, and themass flow detected by the flow sensor 216. Because mass flow remainsrelatively constant through components connected in series, it can beassumed that the mass flow through each of the intake 200, the cleaner202, the compressor 204, and the intercooler 206, along with all pipesupstream from a flow split 226, is equal to the mass flow detected bythe flow sensor 216.

In block 508, which may be a sub-block of block 506, the ECU 102 maycalculate the mass flow, or other flow, values of the gas at the bypassbranch 210 based on a previous bypass pressure value. The ECU 102 maycalculate the flow and pressure values at each of the components of thefuel cell circuit 118 during each timestep. For example, each timestepmay be 0.04 seconds, 0.08 seconds, 0.16 seconds, or the like.

Because the ECU 102 has previously calculated a pressure of the fluidthrough the bypass branch 210, the ECU may use a previously calculatedbypass pressure value that was calculated during a previous timestep inorder to calculate the current flow through the bypass branch 210. Forexample, the ECU may use one or more of equations 1, 2, 3, or 4discussed below to calculate the current flow through the bypass branchusing the previously calculated bypass pressure value as the pressurevalue. During a first iteration of the method 500, the ECU 102 maycalculate the current flow value based on a previously assigned startingpressure value. In some embodiments, the ECU 102 may also or insteadcalculate the current flow value through the fuel cell stack 208 basedon previously determined fuel cell pressure values.

In some situations, the bypass valve 212 may be closed, thus restrictingairflow through the bypass branch 210. In such situations the ECU 102may assume that the mass flow through the fuel cell stack 208 is equalto the mass flow detected by the flow sensor 216.

The ECU 102 may assume that a sum of the flow through the bypass branch210 and through the fuel cell stack 208 is equal to the mass flowdetected by the flow sensor 216. In that regard, the ECU 102 maycalculate the current flow value through the fuel cell stack 208 bysubtracting the flow through the bypass branch 210 from the mass flowdetected by the flow sensor 216.

In block 510, the ECU 102 may calculate or receive an amount of currentthat is output by the fuel cell stack 208. For example, one or moresensor (not shown) may be coupled to the fuel cell stack 208 and maydetect the current output level. As another example, the ECU 102 mayinclude logic for calculating the amount of current output by the fuelcell stack 208 based on various inputs such as airflow through the fuelcell stack 208, a power request of the fuel cell stack 208, or the like.

In block 512, the ECU 102 may determine or calculate a molar fraction ofthe gas at the fuel cell stack 208 based on the current output by thefuel cell stack 208. The molar fraction corresponds to a ratio orfraction that indicates how much of each component is in the gas. Forexample, when the gas is air, the molar fraction may include apercentage of oxygen in the air, a percentage of nitrogen in the air,and the like. In some embodiments, the ECU 102 may assume that the gasflowing into the fuel cell stack 208 is standard air and includes about21% oxygen and 79% nitrogen. The ECU 102 may then use one or moreequation(s) or lookup table(s) to calculate an amount of oxygen consumedby the fuel cell stack 208, to calculate an amount of hydrogen crossingthrough a membrane of the fuel cell stack 208, and to calculate anamount of liquid water and/or water vapor created in a cathode of thefuel cell stack 208. For example, the amount of liquid water and/orwater vapor created in the cathode may be a function of an electricalcurrent request made of the fuel cell stack 208. Based on the results ofthe lookup tables/equations, the ECU 102 may calculate the molarfraction of the gas that is output by the fuel cell stack 208.

Because the fuel cell stack 208 outputs water in addition to theleftover gas, the ECU 102 may assume that the mass flow of the gasflowing into the fuel cell stack 208 is the same as the mass flow of thegas flowing out of the fuel cell stack 208 regardless of the consumptionof the oxygen by the fuel cell stack 208.

The consumption of the oxygen by the fuel cell stack 208, however, mayresult in the gas that is output by the fuel cell stack 208 having adifferent viscosity than the gas that is received by the fuel cell stack208. In that regard and in block 514, the ECU 102 may use an equation orlookup table to determine a viscosity of the gas that is output by thefuel cell stack based on the calculated molar fraction. As will bediscussed below, the viscosity of the gas affects a Reynolds number,which is used to determine the pressures of the gas at locationsthroughout the fuel cell circuit 118.

In block 516, the ECU may determine a Reynolds number of the gas flowingthrough each component of the fuel cell circuit 118. For example, theECU 102 may use an equation similar to equation 1 below to determine theReynolds number.

$\begin{matrix}{{Re} = \frac{\overset{.}{m}D}{A\; \mu}} & {{Equation}\mspace{14mu} 1}\end{matrix}$

In equation 1, Re represents the Reynolds number, i represents the massflow that was determined in blocks 506 and 508, D represents a diameterof the component through which the gas may flow (including the actuatorsand pipes 220), A represents a cross-sectional area of the componentthrough which the gas may flow, and μ represents the dynamic viscosity,which was calculated in block 514. D and A are both known values foreach component and may be stored in a memory.

In block 518, the ECU 102 may calculate the laminar, turbulent, or mixedflow values of the gas through each of the components based on theReynolds number. For example, the flow values may be provided as Darcyfriction factor values. The ECU 102 may determine whether the flowthrough each component is a laminar flow, a turbulent flow, or a mixedflow (i.e., combination of laminar and turbulent flows) based on theReynolds number. For example, if the Reynolds number is greater than anupper flow threshold then the flow is turbulent, meaning that the flowmay be characterized by chaotic changes in pressure and flow velocity.If the Reynolds number is less than a lower flow threshold then the flowis laminar, meaning that the gas flows in parallel layers with little orno disruption between the layers. If the Reynolds number is between thelower flow threshold and the upper flow threshold then the flow exhibitscharacteristics of both laminar flow and turbulent flow and isconsidered to be a mixed flow. The upper flow threshold is a thresholdvalue that indicates whether the flow is purely turbulent (a flow ispurely turbulent when the corresponding Reynolds number is greater thanthe upper flow threshold). The lower flow threshold is a threshold valuethat indicates whether the flow is purely laminar (a flow is purelylaminar when the corresponding Reynolds number is less than the lowerflow threshold).

After determining whether the flow is laminar, turbulent, or mixed, theECU 102 may calculate the flow value using equations 2 and 3 below.Equation 2 is to be used when the flow is turbulent, Equation 3 is to beused when the flow is laminar, and Equations 2 and 3 are to be used whenthe flow is mixed.

$\begin{matrix}{f = \frac{1}{\lbrack {{- 1.8}\mspace{14mu} {\log_{10}( {\frac{6.9}{Re} + ( \frac{Roughness}{3.7\mspace{11mu} D} )^{1.11}} )}} \rbrack^{2}}} & {{Equation}\mspace{14mu} 2}\end{matrix}$

In equation 2, f represents a Darcy friction factor for thecorresponding type of flow (i.e., turbulent). Re represents the Reynoldsnumber that was calculated in block 516. Roughness corresponds to aroughness of the material through which the gas is flowing and is aknown property of the material. D represents a diameter of the componentthrough which the gas may flow (including the actuators and pipes 220).

$\begin{matrix}{f = \frac{64}{Re}} & {{Equation}\mspace{14mu} 3}\end{matrix}$

In equation 3, f represents the Darcy friction factor for thecorresponding type of flow (i.e., laminar) and Re represents theReynolds number that was calculated in block 516.

If the Reynolds number indicates that the flow is a mixed flow then theECU 102 may calculate the value of the flow using a linear interpolationbetween the Darcy friction factor for the laminar flow and the Darcyfriction factor for the turbulent flow (i.e., the results of equations 2and 3). The interpolation may be based on the location of the Reynoldsnumber between the upper flow threshold and the lower flow threshold.For example, the Darcy friction factor for the turbulent flow may beprovided more weight during interpolation of the Reynolds number isnearer to the upper flow threshold than to the lower flow threshold. Asanother example, if the Reynolds number is directly between the upperflow threshold and the lower flow threshold, then the Darcy frictionfactor for the entire flow would be equal to an average of the Darcyfriction factor for the laminar flow and the Darcy friction factor forthe turbulent flow.

In block 520, the ECU 102 may calculate pressure values at an inlet andan outlet of each of the components, including the pipes 220, based onthe laminar, turbulent, or mixed flow values. In particular, if the flowis purely laminar or purely turbulent then the ECU 102 may calculatepressure values using Equation 4 below.

$\begin{matrix}{{\Delta \; P} = \frac{{{\overset{.}{m}}^{2}( {L + {Le}} )}R\; T_{up}f}{2\; {DA}^{2}P_{up}}} & {{Equation}\mspace{14mu} 4}\end{matrix}$

In Equation 4, ΔP represents a pressure drop over the component, whichcorresponds to a difference between pressure at the inlet of thecomponent and at the outlet of the component. L represents a length ofthe component through which the gas flows. Le represents an equivalentlength of the component through which the gas flows. R represents aspecific gas constant of the gas, and has values of

$\frac{Joules}{{mol} \times {Kelvin}}.$

T_(up) represents a temperature of the gas at a high pressure side ofthe component (i.e., a side of the component that experiences, or iscurrently experiencing, higher pressures than the other side). frepresents the Darcy friction factor of the flow calculated in block518. D represents a diameter of the component through which the gas mayflow, and A represents a cross-sectional area of the portion of thecomponent through which the gas may flow. P_(up) represents a pressureof the gas at the high pressure side of the component.

If the flow is a mixed flow, then the ECU 102 may calculate the pressurevalues using Equation 5 below.

$\begin{matrix}{{\Delta \; P} = {{\frac{{Re}_{turb} - {Re}}{{Re}_{turb} - {Re}_{lam}}( \frac{{{\overset{.}{m}}^{2}( {L + {Le}} )}{RT}_{up}}{{f\; 2\; D}{A^{2}P_{up}}} )} + {\frac{{Re} - {Re}_{lam}}{{Re}_{turb} - {Re}_{lam}}( \frac{32\; \overset{.}{m}\; {\mu ( {L - {Le}} )}\; {RT}_{up}}{{AD}^{2}P_{up}} )}}} & {{Equation}\mspace{14mu} 5}\end{matrix}$

In Equation 5, ΔP represents a pressure drop over the component, whichcorresponds to a difference between pressure at the inlet of thecomponent and at the outlet of the component. Re_(turb) represents theupper flow threshold and Re_(lam) represents the lower flow threshold,which were both discussed above with reference to block 518. Rerepresents the Reynolds number calculated in block 516. {dot over (m)}represents the mass flow that was determined in blocks 506 and 508. Lrepresents a length of the component through which the gas flows. Lerepresents an equivalent length of the component through which the gasflows. R represents a specific gas constant of the gas, and has valuesof

$\frac{Joules}{{mol} \times {Kelvin}}.$

T_(up) represents a temperature of the gas at a high pressure side ofthe component. f represents the flow value calculated in block 518. Drepresents a diameter of the component through which the gas may flow,and A represents a cross-sectional area of the portion of the componentthrough which the gas may flow. P_(up) represents a pressure of the gasat the high pressure side of the component.

Equations 4 and 5 above provide pressure drops but not specific pressurevalues at the inlets and outlets of the components. However, the ECU 102may calculate or determine the specific pressure values based on thecalculated pressure drops, the pressure detected by the pressure sensor218, and by assuming that the pressures at an inlet 232 of the intake200 and the outlet 234 of the valves 212, 214 is equal to ambientpressure.

For example, to find the pressure of the gas at an inlet 228 of thecompressor 204 and an outlet 230 of the compressor 204, the ECU 102 mayfirst determine the pressure drop over the intake 200, the first pipe222, the cleaner 202, and the second pipe 224. The ECU 102 may then addor subtract the pressure drop over the intake 200 from the ambientpressure to determine the pressure at an outlet 236 of the intake 200.The ECU may continue in this fashion to determine the inlet and outletpressures of the first pipe 222, the cleaner 202, and the second pipe224 until the pressure at the inlet 228 of the compressor 204 is known.

The ECU 102 may then determine the pressure drop over a third pipe 238,the intercooler 206, and a fourth pipe 240. The ECU 102 may thensubtract or add the pressure drop over the fourth pipe 240 from thepressure detected by the pressure sensor 218 to determine the pressureat an inlet 242 of the intercooler 206. The ECU 102 may continue in thismanner until the pressure at the outlet 230 of the compressor 204 isfound.

The ECU 102 may use a similar strategy to determine the absolutepressure values at the inlet and outlet of the fuel cell stack 208, thevalves 212, 214, and the pipes therebetween.

In block 522, the ECU may implement a rate limiter to limit a rate ofchange of the calculated values. The gas within the fuel cell circuit118 may experience dynamic compressibility, and thus delays may beexperienced between components. Because the equations are used tocalculate values based on an assumption that dynamic compressibilityfails to affect the flow and pressure values, the calculated values mayoccasionally differ from the measured values. In that regard, the ratelimiter may account for such delays. For example, the rate limiter maylimit a rate of change of the pressure at the outlet 230 of thecompressor 204 to a specific rate of change due to the fact that somedelay occurs between the compressor 204 beginning to compress the airand the pressure at the outlet 230 reaching the specified value.

Referring now to FIGS. 2, 4, 6A, and 6B, a method 600 may be used toperform the functions of the path controller 412 of the ECU 102. Themethod 600 may be performed by various components of the system 101 suchas the ECU 102, the memory 104 of FIG. 1, and the like.

In block 602, multiple maps may be stored in a memory. The maps mayinclude a speed map, compressor flow maps, compressor pressure ratiomaps, fuel cell flow rate maps, and compressor torque maps.

With brief reference to FIG. 7, a speed map 700 is shown. The speed map700 corresponds to the compressor of the fuel cell circuit and has an Xaxis that corresponds to mass flow through the compressor, a Y axis thatcorresponds to pressure ratio across the compressor, and multiple speedlines 702 that correspond to different speeds (such as angular velocity)of the compressor. Desirable state changes of the compressor may beplotted on the speed map 700. As shown, a starting state is shown at astarting state 704, and a final target state is shown at a final targetstate 706. As the compressor moves from the starting state 704 to thefinal target state 706, all three of pressure ratio, mass flow, andcompressor speed reduced in value.

The speed map 700 further includes a surge region 710 and a stall region712. It is undesirable for a current state of the compressor to fallwithin the surge region 710 or the stall region 712. In that regard, itmay be desirable to control the state changes of the compressor suchthat any current state remains within an acceptable region 714.

The speed map 700 may include two or more paths including a surge path716, a stall path 718, and a middle path 720. Each of the paths 716,718, 720 extend from a 0 speed state 722 to a maximum speed line 724,and may each represent a desirable state progression of the compressor.

Returning reference briefly to FIG. 6A, one of the compressor flow, thecompressor pressure ratio, the fuel cell flow rate, or the compressortorque may be referred to as a leading, or reference, state. Thereference state may be selected based on importance of the state to thesystem or importance of the state to protection of the hardware. In someembodiments, the reference state may be compressor airflow. Theremaining states may each be following states, meaning that theirprogression is defined based on the leading state.

Referring to FIGS. 7 and 8, an exemplary set of compressor flow maps 800is shown. The set of compressor flow maps 800 may include a surgecompressor flow map 802 corresponding to the surge path 716, a middlecompressor flow map 804 corresponding to the middle path 720, and astall compressor flow map 806 corresponding to the stall path 718. Eachof the compressor flow maps 800 shown in FIG. 8 may correspond tosituations in which the pressure ratio, mass flow rate, and compressorspeed are intended to decrease. The memory may store an additional setof compressor flow maps that correspond to situations in which thepressure ratio, mass flow rate, and compressor speed are intended toincrease. In that regard, the ECU may select the set of compressor flowmaps 800 when the compressor speed is intended to decrease, and mayselect an alternate set of compressor flow maps when the compressorspeed is intended to increase.

If a starting state is located on any of the surge path 716, the middlepath 720, or the stall path 718 then the ECU may select thecorresponding compressor flow map. For example, if the starting state ison the middle path 720 then the ECU may select the middle compressorflow map 804 to control the compressor flow rate.

The memory may store similar sets of maps for each of the compressorpressure ratio, the fuel cell flow rate, and the compressor torque.

As shown, each of compressor flow maps 800 is normalized, havingnormalized Y axis values from 0 to 1 corresponding to a normalizedreference progression (NRP, or normalized reference state value). Inthat regard, the maps 800 may provide a desirable path of the compressorairflow state from any starting state (corresponding to 0) to any finaltarget state (corresponding to 1). Because the compressor airflow stateis the leading state, the X axis of the compressor flow maps 800corresponds to time.

Referring briefly to FIG. 9, an exemplary fuel cell flow rate map 902 isshown. The fuel cell flow rate state is a following state, meaning thatit is progression is based on a completion percentage of the compressorairflow. As shown, the Y axis of the fuel cell flow rate map 902 hasnormalized values from 0 to 1 corresponding to a normalized followerprogression (NFP, or normalized follower state value). However, becausethe fuel cell flow rate state is a following state, the X axis of thefuel cell flow rate map 902 corresponds to the normalized referenceprogression (NRP) of the compressor airflow. In that regard, progressionof the fuel cell flow rate is controlled based on the normalizedreference progression.

Returning reference to FIGS. 4, 6A, and 6B and in block 604, the ECU 102may determine or receive final target values for each of a compressorflow rate, a compressor pressure ratio, a fuel cell flow rate, and acompressor torque. For example, the final target values may be receivedfrom the state mediator 400. The final target values may be set based ona power request of the fuel cell stack, which may correspond to driverinput such as depression of an accelerator pedal, or correspond tocontrol by the ECU 102 in autonomous or semi-autonomous vehicles.

In block 606, the ECU 102 may determine starting or current values foreach of the compressor flow rate, the compressor pressure ratio, thefuel cell flow rate, and the compressor torque. For example, the ECU 102may determine the current values based on one or more of the estimatedvalues 410 from the state estimator 406 or from the actuator controlsignals 418 from the feedforward and feedback control 416.

In block 608, the ECU 102 may select a first set of maps for each of thecompressor flow rate, compressor pressure ratio, fuel cell flow rate,and compressor torque if the final target values are greater than thestarting or current values, and may select a second set of maps at thefinal target values are less than the starting or current values. Forexample and referring to FIGS. 7 and 8, the ECU may select the set ofmaps 800 because the final target state 706 is less than the startingstate 704. In situations in which a final target state is greater than astarting state, the ECU may select an alternate set of compressor flowmaps.

Returning reference to FIGS. 4, 6A, and 6B, the ECU 102 may interpolatea normalized compressor flow value by interpolating the currentcompressor flow rate between a first path and a second path on the speedmap. For example and referring to FIG. 7, the ECU may determine thenormalized compressor flow value by interpolating the current compressorflow rate of the starting state 704 between the stall path 718 and themiddle path 720 because those are the two nearest paths to the startingstate 704.

Returning reference to FIGS. 4, 6A, and 6B, the ECU 102 may createinterpolated maps for the compressor flow rate, the compressor pressureratio, the fuel cell flow rate, and the compressor torque based on thenormalized compressor flow value. For example and referring to FIGS. 7and 8, the normalized compressor flow value may indicate that 75% of thecontrol (or interpolated) path should be based on the stall path 718 and25% of the control path should be based on the middle path 720.

Based on this determination, the ECU 102 may create an interpolatedcompressor flow map 810 by interpolating between the middle compressorflow map 804 and the stall compressor flow map 806 based on thenormalized compressor flow value. In that regard, the interpolatedcompressor flow map 810 may be created by combining the stall compressorflow map 806 with the middle compressor flow map 804 and by weightingthe stall compressor flow map 806 at 75% and the middle compressor flowmap 804 at 25%. The interpolated compressor flow map 810 may indicate adesirable progression of the compressor flow rate based on the specificstarting state 704. The ECU 102 may similarly create interpolated mapsfor each of the compressor pressure ratio, the fuel cell flow rate, andthe compressor torque.

Returning reference to FIGS. 4, 6A, and 6B, the ECU 102 may determine anintermediate target compressor flow rate using the interpolatedcompressor flow map along with Equation 6 below. The ECU may determinethe intermediate target compressor flow rate further based on an amountof time that has elapsed since determining or receiving the final targetcompressor flow rate in block 604.

For example and referring to FIGS. 4, 6A, 6B, and 8, the ECU 102 mayfirst identify the amount of time elapsed since determining the finaltarget compressor flow rate, and then may locate the correspondinglocation on the interpolated compressor flow map 810. For example, theECU 102 may identify that 0.2 seconds have elapsed, and thus maydetermine that the normalized reference progression value thatcorresponds to 0.2 seconds is 0.2.

The ECU 102 may then use the normalized reference progression value of0.2 in Equation 6 below to determine the intermediate target compressorflow rate.

Int_tgt_comp_flow=start+(target−start)*NRP  Equation 6:

In Equation 6, Int_tgt_compflow represents the intermediate targetcompressor flow rate. start corresponds to the starting compressor flowrate determined in block 606, and target corresponds to the final targetcompressor flow rate determined in block 604. NRP represents thenormalized reference progression value.

Returning reference to FIGS. 4, 6A, and 6B and in block 616, the ECU 102may determine a completion percentage of the compressor flow rate fromthe starting compressor flow rate to the final target compressor flowrate. In some embodiments, the completion percentage may correspond to,or be the same as, the normalized reference progression value. In thatregard, the completion percentage may be identified or determined withinblock 614 instead of or in addition to block 616.

In block 618, the ECU 102 may determine intermediate target values forthe follower states based on the corresponding interpolated maps, thestarting values, the target values, and the completion percentage.

Referring again to FIG. 9, the interpolated compressor flow map 810 isshown as the reference, or leading, state map. The fuel cell flow ratemap 902 may likewise be an interpolated fuel cell flow rate map 902 andmay be a follower state map. Furthermore, an interpolated compressorpressure ratio map 904 is also shown as a follower state map. Although acompressor acceleration is not shown, it may also be considered as afollower state and may include one or more corresponding compressoracceleration map.

As shown, the fuel cell flow rate map 902 and the compressor pressureratio map 904 both showed normalized follower progression values (the Yaxis) based on the normalized reference progression of the compressorflow (the X axis). For example, after 0.2 seconds, the normalizedreference progression corresponding to the compressor flow rate (i.e.,the completion percentage) may have a value of 0.2 (i.e., indicating 20%completion). In order to determine an intermediate target fuel cell flowrate, the ECU 102 may first apply the 0.2 normalized referenceprogression value to the fuel cell flow rate map 902, which provides anormalized follower progression (NFP) value of about 0.75.

The ECU 102 may then apply the starting fuel cell flow rate value, thefinal target fuel cell flow rate value, and the normalized followerprogression from the fuel cell flow rate map 902 to equation 7 below.

Int_tgt_fc_flow=start+(target−start)*NFP  Equation 7:

Returning reference to FIGS. 6A and 6B and in Equation 7,Int_tgt_fc_fc_low represents the intermediate target fuel cell flowrate. start corresponds to the starting fuel cell flow rate determinedin block 606 and target corresponds to the final target fuel cell flowrate determined in block 604. NFP represents the normalized followerprogression value of the fuel cell flow rate.

In block 620, the ECU 102 may control the actuators of the fuel cellcircuit (including the compressor and valves) based on the intermediatetarget values. For example, the ECU 102 may control at least one of thecompressor, the bypass valve, or the restriction valve based on theintermediate target values for the compressor flow rate, the compressorpressure ratio, the fuel cell flow rate, and the compressor torque.

In block 622, the ECU 102 may continue to determine intermediate targetvalues and to control the actuators to achieve the intermediate targetvalues until the intermediate target values are the same as the finaltarget values, or new final target values are determined or received.

In some embodiments, compressor acceleration may be an additionalfollower state, such that the ECU 102 may determine intermediate targetvalues for the compressor acceleration based on interpolated maps, astarting value, a target value, and the completion percentage. Theacceleration rate may be provided as a desired acceleration rate of thecompressor, as a desired acceleration torque of the compressor, or both.In some embodiments, the path controller 412 of FIG. 2 may determine thedesired acceleration using a method other than setting the desiredacceleration as a follower state.

Referring now to FIG. 10, an exemplary usage of the method 600 of FIGS.6A and 6B is shown. FIG. 10 illustrates the interpolated compressor flowmap 810, the interpolated pressure ratio map 904, and graphs 1006plotting the intermediate target pressure ratio values at 3 differenttimes. A first row 1000 illustrates the status at 0 seconds, a secondrow 1002 illustrates the status at 0.3 seconds, and a third row 1004illustrates the status at 0.6 seconds.

As shown in the first row 1000, the normalized reference progression onthe interpolated compressor flow rate map 810 is 0 because the time isequal to 0. Accordingly, the normalized follower progression of theinterpolated pressure ratio map 904 is also 0 due to the normalizedreference progression being 0. Thus, plugging these values into Equation7 yields an intermediate target value of about 2.8, which corresponds tothe starting value (because the normalized follower progression value is0, the term (target−start)*NFP is also 0, thus leaving the result ofEquation 7 as start).

As shown in the second row 1002, the normalized reference progression onthe interpolated compressor flow map 810 is about 0.4, which isdetermined by applying 0.3 seconds to the interpolated compressor flowrate map 810. Accordingly, the normalized follower progression of theinterpolated pressure ratio map 904 is equal to about 0.65, whichcorresponds to the normalized reference progression value of 0.4. Thus,plugging these values into Equation 7 yields an intermediate pressureratio target value of about 1.3.

As shown in the third row 1004, the normalized reference progression onthe interpolated compressor flow rate map 810 is 1, which is determinedby applying 0.6 seconds to the interpolated compressor flow rate map810. Accordingly, the normalized follower progression of theinterpolated pressure ratio map 904 is equal to 1, which corresponds tothe normalized reference progression value of 1. Thus, plugging thesevalues into Equation 7 yields an intermediate pressure ratio targetvalue of 1. Accordingly, the method 600 of FIGS. 6A and 6B may terminateor restart due to the intermediate pressure ratio target value beingequal to the final target pressure ratio value.

Referring now to FIGS. 2, 4, and 11, a method 1100 may be performed bythe ECU 102, such as by the feedforward and feedback control 416, toperform a feedforward control of either of the restriction valve 214 orthe bypass valve 212. In that regard, a first instance of the method1100 may be used to perform feedforward control of the restriction valve214, and a second instance of the method 1100 may be used to performfeedforward control of the bypass valve 212.

In block 1102, the ECU 102 may determine or receive a desired pressureof the gas within the fuel cell circuit. For example, the desiredpressure may correspond to a desired pressure at an inlet 244 or anoutlet 246 of the fuel cell stack 208, at the inlet 228 or the outlet230 of the compressor 204, or the like. For example, the desiredpressure may be determined by the state mediator 400 and may be based onthe control signal 402.

In block 1104, the ECU 102 may determine a desired mass flow rate of thegas through a corresponding valve (either the restriction valve 214 orthe bypass valve 212) based on the desired pressure of the gas that wasdetermined or received in block 1102. For example, the desired pressuremay correspond to a desired pressure at the outlet 246 of the fuel cellstack 208. In that regard, the ECU 102 may calculate a desired mass flowof the gas through the restriction valve 214 that will cause thepressure at the outlet 246 of the fuel cell stack 208 to reach thedesired pressure. For example, the ECU 102 may determine the desiredmass flow rate using an equation similar to Equation 4 above.

In some embodiments, the path controller 412 may determine the desiredmass flow rate of the gas through the valve. The desired mass flow ratemay correspond to an intermediate target mass flow rate as determined bythe path controller 412. For example, the path controller 412 maydictate or provide desired pressure values and desired mass flow valuesof the gas through the components of the fuel cell circuit 118 (such asthe bypass valve 212 and the restriction valve 214).

In some embodiments, the state estimator 406 may then calculate ordetermine the pressure and flow values at each component of the fuelcell circuit 118 that are currently unknown, and calculate or determinethe pressure and flow values at each component if the system achievesthe target state. For example, the state estimator 406 may calculate ordetermine the pressure and flow values at each component if thecorresponding valve is set to the desired mass flow rate.

In block 1106, the ECU 102 may determine a current Reynolds numbercorresponding to the gas flowing through the valve. For example, the ECU102 may determine the current Reynolds number using an equation similarto Equation 1 above.

In block 1108, the ECU 102 may determine a current laminar, subsonic, orchoked flow. For example, the ECU 102 may determine the current laminar,subsonic, or choked flow based on the Reynolds number. Initially, theECU 102 may determine whether the flow through the valve is laminar,subsonic, or choked. If the Reynolds number is within a first range ofvalues then the ECU 102 may determine that the flow is laminar. If theReynolds number is within a second range of values then the ECU 102 maydetermine that the flow is subsonic. If the Reynolds number is within athird range of values then the ECU 102 may determine that the flow ischoked.

After determining whether the flow is laminar, subsonic, or choked, theECU 102 may determine the specific flow value using one or more ofEquations 8 through 10 below.

$\begin{matrix}{\Psi = {\sqrt{\frac{2\; \gamma}{( {\gamma - 1} )}*( {B_{lam}^{\frac{2}{\gamma}} - B_{lam}^{\frac{({\gamma - 1})}{\gamma}}} )}\frac{( {1 - \frac{P_{d}}{P_{u}}} )}{( {1 - B_{lam}} )}}} & {{Equation}\mspace{14mu} 8}\end{matrix}$

Equation 8 is to be used when the flow is a laminar flow. In equation 8,ψ represents the laminar flow value. γ represents a specific heat ratioof the gas flowing through the valve, and corresponds to a ratio ofspecific heat of the gas at constant volume to specific heat of the gasat constant pressure. B_(lam) represents a pressure ratio above whichthe flow is assumed to be laminar. P_(u) represents a pressure of thegas at a low pressure side of the corresponding valve, and P_(u)represents a pressure of the gas at a high pressure side of thecorresponding valve.

$\begin{matrix}{\Psi = \sqrt{\frac{2\; \gamma}{( {\gamma - 1} )}( {\frac{P_{d}^{\frac{2}{\gamma}}}{P_{u}} - \frac{P_{d}^{\frac{({\gamma - 1})}{\gamma}}}{P_{u}}} )}} & {{Equation}\mspace{14mu} 9}\end{matrix}$

Equation 9 is to be used when the flow is a subsonic flow. The variablesused in Equation 9 have the same meaning as the corresponding variablesin Equation 8, except that W represents the subsonic flow value.

$\begin{matrix}{\Psi = \sqrt{\gamma*B_{cr}^{\frac{({\gamma - 1})}{\gamma}}}} & {{Equation}\mspace{14mu} 10}\end{matrix}$

Equation 10 is to be used when the flow is a choked flow. The variablesused in Equation 10 have the same meanings as the correspondingvariables in Equation 8, except that ψ represents the choked flow value.The newly introduced variable, B_(cr) represents a critical pressureratio and may be calculated using equation 11 below.

$\begin{matrix}{B_{cr} = \frac{2^{\frac{\gamma}{({\gamma - 1})}}}{( {\gamma + 1} )}} & {{Equation}\mspace{14mu} 11}\end{matrix}$

In Equation 11, γ has the same meaning described above with reference toEquation 8.

After determining the current laminar, subsonic, or choked flow, the ECU102 may calculate a desired valve area to achieve the desired mass flowrate in block 1110. The desired valve area corresponds to across-sectional area of the valve through which the gas may flow. Thecross-sectional area may be changed by adjusting the valve position. TheECU 102 may solve Equation 12 below for the desired valve area.

$\begin{matrix}{\overset{.}{m} = {{Cd}\frac{A}{\sqrt{R_{s}*T_{u}}}P_{u}\Psi}} & {{Equation}\mspace{14mu} 12}\end{matrix}$

In equation 12, {dot over (m)} is the desired mass flow rate. Cd is adischarge coefficient. A is the desired valve area for which the ECU 102may solve. R_(s) is a specific gas constant. T_(u) is a temperature atthe high pressure side of the valve and P_(u) is a pressure at the highpressure side of the valve. Ψ is the current laminar, subsonic, orchoked flow that was calculated in block 1108.

The memory 104 of FIG. 1 may store a map or function that associatesdesired valve areas with corresponding valve positions. In that regardand in block 1112, the ECU 102 may compare the desired valve area thatwas calculated in block 1110 to the map or function to determine adesired valve position that corresponds to the desired valve area.Stated differently, causing the valve to have the desired valve positionin turn causes the valve to have the desired valve area and, thus,achieve the desired mass flow through the valve.

In some embodiments, the function may include an equation such that theECU 102 may solve the equation using the desired valve area to determinethe desired valve position. For example, the ECU 102 may use an equationsimilar to Equation 13 below to solve for the desired valve position orto populate a map that associates desired valve areas with desired valvepositions.

$\begin{matrix}{A = {{( \frac{\pi \; D}{2} )^{2}c} + A_{0}}} & {{Equation}\mspace{14mu} 13}\end{matrix}$

In Equation 13, A is the desired valve area. Referring briefly to FIG.12, an exemplary valve 1200, which may similar to the same as the bypassvalve 212 or the restriction valve 214, is shown to illustrate thevarious parameters of the equations. In Equation 13, D is a diameter1202 of the valve 1200. A₀ is a throttle leak area. c is an independentvariable and is shown in Equation 14 below.

$\begin{matrix}{c = {1 - b + {\frac{2}{\pi}\lbrack {{a\sqrt{1 - ( \frac{a}{b} )^{2}}} - {b\mspace{11mu} {asin}\; ( \frac{a}{b} )} - {a\sqrt{1 - (a)^{2}}} + {{asin}(a)}} \rbrack}}} & {{Equation}\mspace{14mu} 14}\end{matrix}$

In Equation 14, a is provided in Equation 15 below, and b is provided inEquation 16 below.

$\begin{matrix}{a = \frac{t}{D}} & {{Equation}\mspace{14mu} 15}\end{matrix}$

In Equation 15, t is a throttle shaft diameter illustrated as a throttleshaft diameter 1204 of the valve 1200. D again represents the diameter1202.

$\begin{matrix}{b = \frac{\cos (\alpha)}{\cos ( \alpha_{0} )}} & {{Equation}\mspace{14mu} 16}\end{matrix}$

In Equation 16, α is an angle 1208 between a valve plate 1210 and alongitudinal axis 1212 and corresponds to a throttle angle of the valve1200. α₀ is an angle 1206 between the valve plate 1210 and a line 1214perpendicular to the axis 1212, and corresponds to a closed throttleangle. α and α₀ may both be measured in radians.

Returning reference to FIGS. 2, 4, and 11, the ECU 102 may solveEquations 13-16 to determine the desired valve position. For example,the ECU 102 may first solve Equation 13 for A, the desired valve area.Based on the value of A, the ECU 102 may then solve Equation 14 toidentify the value of b, and may then solve Equation 16 for a.

After the ECU 102 determines the desired valve position, the ECU maycontrol the valve in block 1114 to have the desired valve position. Inthat regard, after the ECU controls the valve to have the desired valveposition, the mass flow through the valve may be near the desired massflow value determined in block 1104. The ECU 102 may perform the method1100 once for the bypass valve 212 and may perform the method 1100 againfor the restriction valve 214. In some embodiments, the ECU 102 mayperform two instances of the method 1100 simultaneously (i.e., mayperform a first instance of the method 1100 for the bypass valve 212 andsimultaneously perform a second instance of the method 1100 for therestriction valve 214).

Referring now to FIGS. 2, 4, 13A, and 13B, a method 1300 may be used bythe ECU 102, such as in the feedforward or feedback control 416, toperform a feedforward control of the compressor 204. The control of thecompressor 204 may include both a speed control and a torque control.Although the method 1300 illustrates the speed control and the torquecontrol occurring one after the other, one skilled in the art willrealize that the speed control and the torque control may be performedsimultaneously or may be performed one after the other.

In block 1302, a speed map, such as the speed map the 700 of FIG. 7, maybe stored in the memory. The speed map may associate desired compressorflow rates and desired compressor pressure ratios with correspondingdesired, or target, compressor speeds.

In block 1304, the ECU 102 may determine or receive a desired compressorflow rate and a desired compressor pressure ratio corresponding to apressure ratio across the compressor 204. For example, the desiredcompressor flow rate and the desired compressor pressure ratio may bereceived from the path controller 412.

In block 1306, the ECU 102 may compare the desired flow rate and thedesired pressure ratio to the speed map to determine a desiredcompressor speed. In some embodiments, the ECU 102 may calculate thedesired compressor speed based on the desired flow rate and the desiredpressure ratio.

After calculating the desired compressor speed, the ECU 102 may controlthe compressor 204 to achieve the desired compressor speed in block1308.

In block 1310, the ECU 102 may determine or receive a current desiredcompressor speed corresponding to a desired compressor speed at acurrent timestep. For example, the current desired compressor speed maybe received from the path controller 412.

In block 1312, the ECU 102 may determine or receive a future desiredcompressor speed corresponding to a future timestep. In someembodiments, the future timestep may be a timestep immediately after thecurrent timestep and, in some embodiments, the future timestep may bemultiple timesteps beyond the current timestep. The future desiredcompressor speed may likewise be received from the path controller 412.

In block 1314, the ECU 102 may calculate a speed difference between thecurrent desired compressor speed and the future desired compressorspeed.

For example and with brief reference to FIGS. 13A, 13B, and 14, acontrol system 1400 may be used to perform the operations of block 1310through block 1314. In particular, a desired compressor speed 1402 maybe received. The desired compressor speed 1402 may be received by acomparator 1404. The desired compressor speed 1402 may likewise bereceived by a first unit delay block 1406 and a second unit delay block1408. Each of the first unit delay block 1406 and the second unit delayblock 1408 may delay the received desired compressor speed 1402 by oneor more timestep. In that regard, the output of the second unit delayblock 1408 may be referred to as a previous desired compressor speed1410 and the desired compressor speed 1402 may be referred to as acurrent desired compressor speed 1402 as it corresponds to a later pointin time than the previous desired compressor speed 1410. In someembodiments, the output of the second unit delay block 1408 may bereferred to as a current desired compressor speed, and the desiredcompressor speed 1402 may be referred to as a future desired compressorspeed, due to the fact that the desired compressor speed 1402corresponds to a desired speed that is in the future relative to thespeed output by the second unit delay block 1408.

The comparator 1404 may compare the previous (or current) desiredcompressor speed 1410 and the current (or future) desired compressorspeed 1402 and output a speed difference 1412 corresponding to adifference between the two.

Returning reference to FIGS. 2, 4, 13A, and 13B, and in block 1316, theECU 102 may determine a time delay between the current timestep and thefuture timestep, corresponding to an amount of time between the two.

In block 1318, the ECU 102 may determine or receive a desiredacceleration rate of the compressor. The desired acceleration rate maycorrespond to the speed difference determined in block 1314 along withthe time delay determined in block 1316. In particular, the ECU 102 maydivide the speed difference by the time delay. The result of thisdivision provides units of acceleration that correspond to the desiredacceleration rate.

In some embodiments and as described above, the path controller 412 mayprovide intermediate target compressor acceleration values, which may beused as the desired acceleration rate. In that regard, blocks 1310through 1318 may be replaced with a block that receives the desiredacceleration rate from the path controller 412. In some embodiments, thepath controller 412 may provide the desired acceleration torque of thecompressor instead of, or in addition to, the desired acceleration rate.

In block 1320, the ECU may determine a desired acceleration torque ofthe compressor based on the desired acceleration rate that wasdetermined in block 1318. In particular, the ECU 102 may use an equationsimilar to Equation 17 below to determine the desired accelerationtorque of the compressor 204.

τ_(acceleration) =Iα  Equation 17:

In Equation 17, τ_(acceleration) is the desired acceleration torque ofthe compressor 204. I is an equivalent inertia, and may have units suchas kg*m². The equivalent inertia may correspond to inertia of thecomponents of the compressor 204 such as the gearbox, the shaft, theairfoil, and the like. α is the angular acceleration, which may bedetermined based on the desired acceleration rate of the compressor 204.

In block 1322, the ECU 102 may determine an efficiency of the compressor204. For example, a memory may store an efficiency map that associatescompressor flow values and compressor pressure ratio values tocorresponding efficiencies. In that regard, the ECU 102 may determinethe efficiency of the compressor 204 by applying a current compressorflow value and a current compressor pressure ratio to the efficiency mapto retrieve the current efficiency.

In block 1324, the ECU 102 may determine a compression torque of thecompressor 204 based on the efficiency that was determined in block1322. For example, the ECU 102 may use an equation similar to Equation18 below to calculate the compression torque.

$\begin{matrix}{\tau_{compression} = {\overset{.}{m}\; C_{P}{T_{i\; n}( {( \frac{P_{out}}{P_{i\; n}} )^{\frac{\gamma - 1}{\gamma}} - 1} )}\mspace{11mu} \frac{( \frac{1}{Eff} )}{\omega}}} & {{Equation}\mspace{14mu} 18}\end{matrix}$

In equation 18, τ_(compression) is the compression torque of thecompressor 204. {dot over (m)} is a desired mass flow of the gas throughthe compressor 204, and may be received from the path controller 412.C_(p) is a specific heat of the gas within the compressor 204. T_(in) isthe temperature of the gas at the inlet 228 of the compressor 204.P_(out) is a target pressure of the gas at the outlet 230 of thecompressor 204, and P_(in) is a target pressure of the gas at the inlet228 of the compressor 204. P_(out) and P_(in) may be received from thepath controller 412. γ represents a specific heat ratio of the gasflowing through the valve, and corresponds to a ratio of specific heatof the gas at constant pressure to specific heat of the gas at constantvolume. Eff is the efficiency that was determined in block 1322. ω isthe compressor speed, which may be measured in radians per second. TheECU 102 may calculate ω using Equation 19 below.

In some embodiments, a map may be created for compression torque byperforming calculations with changing variable values and storing theresults in the map. In that regard, the ECU 102 may receive at least oneof a compressor speed or a compressor ratio, may compare the speed andpressure ratio to the map, and may determine the compression torquebased on the comparison to the map.

$\begin{matrix}{\omega = {{ACP}_{spd}2\; \frac{\pi}{60}\; g_{ratio}}} & {{Equation}\mspace{14mu} 19}\end{matrix}$

In Equation 19, ω is the compressor speed. ACP_(spd) is the motor speedof the motor of the compressor 204 (such as the motor 306 of thecompressor 300 of FIG. 3). g_(ratio) is a current gear ratio of thegearbox of the compressor (such as the gearbox 308 of the compressor 300of FIG. 3).

In block 1326, the ECU 102 may determine a friction torque of thecompressor 204. For example, the ECU may use an equation similar toEquation 20 below to calculate the friction torque.

τ_(friction)=visC_(coef)ω+Col_(trq)+(brkwy_(trq)−Col_(trq))e^((−trans)^(coef) ^(ω))  Equation 20:

In Equation 20, τ_(friction) is the friction torque. visc_(coef),Col_(trq), brkwy_(trq), and trans_(coef) are tuned constant values. ω isthe compressor speed that was calculated in Equation 19 above.

In some embodiments, a map may be created for friction torque byperforming calculations with changing variable values and storing theresults in the map. In that regard, the ECU 102 may receive at least oneof a compressor speed or a compressor pressure ratio, may compare thespeed and pressure ratio to the map, and may determine the frictiontorque based on the comparison to the map.

In some embodiments, a map may be created for combined friction andcompression torque values by performing calculations with changingvariable values and storing the results in the map. In that regard, theECU 102 may receive a compressor speed and a compressor pressure ratio,may compare the speed and pressure ratio to the map, and may determinethe combined friction and compression torque value based on thecomparison to the map.

In block 1328, the ECU 102 may determine a total desired compressortorque based on the desired acceleration torque, the compression torque,and the friction torque. For example, the ECU 102 may determine thetotal desired compressor torque by adding each of the desiredacceleration torque, the compression torque, and the friction torquetogether.

In block 1330, the ECU 102 may control the compressor to have the totaldesired compressor torque that was determined in block 1328.

Referring now to FIGS. 2, 4, 15A, and 15B, a method 1500 may be used bythe ECU 102, such as in the feedforward or feedback control 416, toperform a feedback control of the bypass valve 212 and the restrictionvalve 214. In particular, the ECU 102 may compare the current and targetvalues and identify a feedback control based on a difference between thecurrent and target values. For example, the values may include apressure at an outlet 246 of the fuel cell stack 248 for controlling therestriction valve 214, and a pressure ratio across the bypass valve 212for controlling the bypass valve 212.

In particular and in block 1502, the ECU 102 may store a pressure mapthat associates pressure values with corresponding valve positions. Forexample and referring to FIGS. 2, 16A and 16B, a first pressure map 1600associates pressure at the outlet 246 of the fuel cell stack 208 (alongthe X axis) with a valve position of the restriction valve 214 (alongthe Y axis). In that regard, a valve position corresponding to a valveposition of the restriction valve 214 may be retrieved from the firstpressure map 1600 based on a received pressure value.

Likewise, a second pressure map 1650 associates pressure ratio acrossthe bypass valve 212 (along the X axis) with a valve position of thebypass valve 212 (along the Y axis). In that regard, a valve positioncorresponding to a valve position of the bypass valve 212 may bereceived from the second pressure map 1650 based on a received pressureratio.

Returning reference to FIGS. 2, 4, 15A, and 15B and in block 1504, theECU 102 may determine or receive a desired pressure value of the gas inthe fuel cell circuit. The desired pressure value may correspond to apressure at the outlet 246 of the fuel cell stack 208 or a pressureratio across the bypass valve 212.

In block 1506, the ECU 102 may determine or receive a current pressurevalue of the gas in the fuel cell circuit. Again, the current pressurevalue may correspond to a pressure at the outlet 246 of the fuel cellstack 208 or a pressure ratio across the bypass valve 212.

In block 1508, the ECU 102 may apply the desired pressure value to thepressure map to determine a desired valve position. For example, the ECU102 may apply the desired pressure at the outlet 246 of the fuel cellstack 208 to the first pressure map 1600 to determine a desired valveposition of the restriction valve 214. Likewise, the ECU 102 may applythe desired pressure ratio across the bypass valve 212 to the secondpressure map 1650 to determine a desired valve position of the bypassvalve 212.

In block 1510, the ECU 102 may apply the current pressure value to thepressure map to determine a current valve position. This may be done foreach of the restriction valve 214 and the bypass valve 212.

In block 1512, the ECU 102 may compare the current pressure value to thetarget pressure value to identify a different signal corresponding to adifference between the current pressure value and the target pressurevalue. The ECU 102 may perform this operation for each of therestriction valve 214 and the bypass valve 212.

In block 1514, the ECU 102 may apply a proportional-integral-derivative(PID, or PI) controller to the different signal to determine a desiredadjustment to the valve position. The PID controller may analyze pastand present values of the error signal and generate the feedback controlsignal based on present error values, past error values, and potentialfuture errors of the error signal.

Referring now to FIGS. 2, 4, 16A, and 17A, a control 1700 may be used bythe ECU 102 to perform feedback control of the restriction valve 214using a method similar to the method 1500 of FIGS. 15A and 15B.

In the control 1700, the ECU 102 may receive or determine a target fuelcell pressure 1702 corresponding to a target or desirable pressure atthe outlet 246 of the fuel cell stack 208. For example, the target fuelcell pressure 1702 may be determined by the state mediator 400. The ECU102 may further determine or receive a current fuel cell pressure 1704corresponding to a current pressure at the outlet 246 of the fuel cellstack 208. For example, the current fuel cell pressure 1704 may bereceived from the state estimator 406.

The ECU 102 may then pass the target fuel cell pressure 1702 through thefirst pressure map 1600 to determine a target or desired valve position1706 that corresponds to the target fuel cell pressure 1702. The ECU 102may likewise pass the current fuel cell pressure 1704 through the firstpressure map 1600 to determine a current valve position 1708 thatcorresponds to the current fuel cell pressure 1704.

The target or desired valve position 1706 and the current valve position1708 may be received by a difference block 1710. The difference block1710 may identify a difference between the target or desired valveposition 1706 and the current valve position 1708, and may output thedifference as a different signal 1712.

The different signal 1712 may be received by a PID controller 1714. ThePID controller 1714 may analyze past and present values of thedifference signal and generate a feedback adjustment signal 1716 thatcorresponds to a desired adjustment to the valve position of therestriction valve 214.

Referring now to FIGS. 2, 4, 16B, and 17B, a control 1750 may be used bythe ECU 102 to perform feedback control of the restriction valve 214using a method similar to the method 1500 of FIGS. 15A and 15B.

In the control 1750, the ECU 102 may receive or determine a targetbypass valve pressure ratio 1752 corresponding to a target or desirablepressure ratio across the bypass valve 212. For example, the targetbypass valve pressure ratio 1752 may be determined by the state mediator400. The ECU 102 may further determine or receive a current bypass valvepressure ratio 1754 corresponding to a current pressure ratio across thebypass valve 212. For example, the current bypass valve pressure ratio1754 may be received from the state estimator 406.

The ECU 102 may then pass the target bypass valve pressure ratio 1752through the second pressure map 1615 to determine a target or desiredvalve position 1756 that corresponds to the target bypass valve pressureratio 1752. The ECU 102 may likewise pass the current bypass valvepressure ratio 1754 through the second pressure map 1650 to determine acurrent valve position 1758 that corresponds to the current bypass valvepressure ratio 1754.

The target or desired valve position 1756 and the current valve position1758 may be received by a difference block 1760. The difference block1760 may identify a difference between the target or desired valveposition 1756 and the current valve position 1758, and may output thedifference as a different signal 1762.

The different signal 1762 may be received by a PID controller 1764. ThePID controller 1764 may analyze past and present values of the errorsignal and generate a feedback adjustment signal 1766 that correspondsto a desired adjustment to the valve position of the bypass valve 212.

Returning reference to FIGS. 2, 4, 15A, and 15B and in block 1516, theECU 102 may delay applying the integral term of the PID controller untilthe different signal has reduced by a predetermined threshold in orderto reduce overshoot of the desired adjustment due to a phenomena calledintegral windup. Sometimes, when a difference signal is relativelylarge, the integral term may be very large initially, along with theproportional term. As the difference signal approaches 0, theproportional term shrinks but the integral term remains relativelylarge. Thus, the initial large size of the integral term maysufficiently accumulate to overshoot the desired adjustment.

By delaying application of the integral term of the PID controller, theintegral term may be introduced when the difference signal is relativelysmall. In that regard, the predetermined threshold may correspond to athreshold difference below which integral windup is unlikely to occur.In that regard, block 1516 may be referred to as integral windupprotection, and may be optional within the method 1500.

In addition to, or instead of, performing the integral windupprotection, the ECU 102 may implement what may be referred to as“learning values” in blocks 1518 and 1520. In particular and in block1518, when the difference signal converges to or near 0 (i.e., when thecurrent pressure value is substantially equal to the desired pressurevalue) for a given target pressure value, then the ECU 102 may store thefinal integral term from the PID controller in a memory.

In block 1520, during a subsequent convergence towards the same giventarget pressure value, the ECU 102 may cause the PID controller to beginthe convergence using the stored final integral term. By storing thefinal integral term, each convergence towards the same given targetpressure value is likely to begin with an integral term (i.e., thestored final integral term) that is relatively close to a value that islikely to provide relatively quick and accurate convergence towards thegiven target pressure value.

In block 1522, the ECU 102 may adjust the corresponding valve (i.e., therestriction valve 214 or the bypass valve 212) based on the desiredadjustment to the valve position. In some embodiments, the ECU 102 mayadd the desired adjustment to the valve position to a feedforwardcontrol signal and control the corresponding valve based on the resultsof the addition. In some embodiments, the ECU 102 may simply adjust thecontrol of the corresponding valve using the desired adjustment to thevalve position.

Referring now to FIGS. 2, 4, 18A, and 18B, a method 1800 may be used bythe ECU 102, such as in the feedforward or feedback control 416, toperform a feedback control of the compressor 204. In particular, the ECU102 may compare the current and target values and identify a feedbackcontrol signal based on a difference between the current and targetvalues. For example, the values may include a total airflow through thecompressor 204.

In particular and in block 1802, the ECU 102 may store an airflow mapthat associates airflow values with corresponding compressor speeds. Forexample and referring to FIGS. 2 and 19, an airflow map 1900 associatesairflow through the compressor 204 (along the X axis) with a compressorspeed (along the Y axis). In that regard, a compressor speedcorresponding to a speed of the compressor 204 may be retrieved from theairflow map 1900 based on a received airflow value.

Returning reference to FIGS. 2, 4, 18A, and 18B and in block 1804, theECU 102 may determine or receive a desired compressor flow ratecorresponding to a total airflow through the compressor 204. In block1806, the ECU 102 may determine or receive a current compressor flowrate.

In block 1808, the ECU 102 may apply the desired compressor flow rate tothe airflow map to determine a desired compressor speed. In block 1810,the ECU 102 may apply the current compressor flow rate to the airflowmap to determine a current compressor speed.

In block 1812, the ECU 102 may compare the current compressor speed tothe target compressor speed to identify a different signal correspondingto a difference between the current compressor speed and the targetcompressor speed.

In block 1814, the ECU 102 may apply a PID controller to the differentsignal to determine a desired adjustment to the compressor speed.

Referring now to FIGS. 2, 4, 19, and 20A, a control 2000 may be used bythe ECU 102 to perform feedback control of the compressor speed of thecompressor 204 using a method similar to the method 1800 of FIGS. 18Aand 18B.

In the control 2000, the ECU 102 may receive or determine a target totalcompressor airflow 2002 corresponding to a target or desirable totalflow of the gas through the compressor 204. For example, the targettotal compressor airflow 2002 may be determined by the state mediator400. The ECU 102 may further determine or receive a current totalcompressor airflow 2004 corresponding to current total flow through thecompressor 204. For example, the current total compressor flow 2004 maybe received from the state estimator 406.

The ECU 102 may then pass the target total compressor flow 2002 throughthe airflow map 1900 to determine a target or desired compressor speed2006 that corresponds to the target total compressor airflow 2002. TheECU 102 may likewise pass the current total compressor flow 2004 throughthe airflow map 1900 to determine a current compressor speed 2008 thatcorresponds to the current total compressor airflow 2004.

The target or desired compressor speed 2006 and the current compressorspeed 2008 may be received by a difference block 2010. The differenceblock 2010 may identify a difference between the target or desiredcompressor speed 2006 and the current compressor speed 2008, and mayoutput the difference as a difference signal 2012.

The difference signal 2012 may be received by a PID controller 2014. ThePID controller 2014 may analyze past and present values of thedifference signal 2012 and may generate a feedback speed adjustmentsignal 2016 that corresponds to a desired adjustment to the compressorspeed of the compressor 204.

Returning reference to FIGS. 2, 4, 18A, and 18B and in block 1816, theECU 102 may delay applying the integral term of the PID controller untilthe different signal has reduced by a predetermined threshold in orderto reduce overshoot of the desired adjustment due to integral windup.This may be performed in a similar manner as block 1516 of FIGS. 15A and15B.

In addition to, or instead of, performing the integral windupprotection, the ECU 102 may implement “learning values” in blocks 1818and 1820. This may be performed in a similar manner as block 1518 and1520 of FIGS. 15A and 15B.

In block 1822, the ECU 102 may adjust the compressor speed based on thedesired adjustment to the compressor speed. This may be performed in asimilar manner as block 1522 of FIGS. 15A and 15B.

As described above, the compressor 204 may have a compressor speed and acompressor torque which may be controlled separately. In that regard,blocks 1824 through 1830 may be used to control the compressor torque ofthe compressor 204.

The compressor speed and compressor torque may be related such that thecompressor torque may be directly proportional to the compressor speed.In that regard and in block 1824, the ECU 102 may determine a desiredcompressor torque value based on the desired compressor speed. Forexample, the desired compressor speed may be determined in block 1808.In order to determine the desired compressor torque, the desiredcompressor speed may be applied to a map, in a similar manner as thecompressor speed is determined based on total air flow. However, due tothe proportional relationship between the torque and speed of thecompressor 204, a proportional gain may be applied to the desiredcompressor speed to obtain the desired compressor torque.

Likewise, in block 1826, the ECU 102 may determine a current compressortorque value based on the current compressor speed. The currentcompressor speed may be determined in block 1810. The ECU 102 maydetermine the current compressor torque either using a map or using aproportional gain, as described above with reference to block 1824.

In block 1828, the ECU 102 may identify a torque difference signalcorresponding to a torque difference between the desired compressortorque value and the current compressor torque value.

In block 1830, the ECU 102 may apply a PID controller to the differentsignal to determine a desired adjustment to the compressor torque.

In some embodiments, the ECU 102 may implement one or both of integralwindup protection or “learning values.”

In block 1832, the ECU 102 may adjust the compressor torque value of thecompressor based on the desired adjustment to the compressor torque.

Referring now to FIGS. 2, 4, and 20B, a control 2050 may be used by theECU 102 to perform feedback control of the compressor torque of thecompressor 204 using a method similar to the method 1800 of FIGS. 18Aand 18B.

In the control 2050, the ECU 102 may determine a target or desiredcompressor speed 2052 along with a current compressor speed 2054. Thesevalues may be determined or received from any of the feedforward andfeedback control 416, the state estimator 406, or the path controller412.

The ECU 102 may then pass the target compressor speed 2052 through afunction 2056 to determine a target or desired compressor torque 2060.The function 2056 may include a map or a calculation, such as acalculation to apply a proportional gain to the target compressor speed2052. The ECU 102 may likewise pass the current compressor speed 2054through the function 2056 to determine a current compressor torque 2062.

The target or desired compressor torque 2060 and the current compressortorque 2062 may be received by a difference block 2064. The differenceblock 2064 may identify a torque difference signal 2066 that correspondsto a difference between the target or desired compressor torque 2060 andthe current compressor torque 2062.

The torque difference signal 2066 may be received by a PID controller2068. The PID controller 2068 may analyze past and present values of thetorque difference signal 2066 and may generate a feedback torqueadjustment signal 2070 that corresponds to a desired adjustment to thecompressor torque of the compressor 204.

Where used throughout the specification and the claims, “at least one ofA or B” includes “A” only, “B” only, or “A and B.” Exemplary embodimentsof the methods/systems have been disclosed in an illustrative style.Accordingly, the terminology employed throughout should be read in anon-limiting manner. Although minor modifications to the teachingsherein will occur to those well versed in the art, it shall beunderstood that what is intended to be circumscribed within the scope ofthe patent warranted hereon are all such embodiments that reasonablyfall within the scope of the advancement to the art hereby contributed,and that that scope shall not be restricted, except in light of theappended claims and their equivalents.

What is claimed is:
 1. A system for providing oxygen to a fuel cellcircuit, comprising: a compressor configured to pump a gas through thefuel cell circuit; a fuel cell stack having a plurality of fuel cellsand configured to receive the gas; a plurality of pipes each configuredto transport the gas throughout a portion of the fuel cell stack; apressure sensor configured to detect a detected pressure of the gas at afirst location of the fuel cell circuit; a memory configured to store amodel of the fuel cell circuit; and an electronic control unit (ECU)coupled to the compressor, the pressure sensor, and the memory, andconfigured to: determine or receive a control signal corresponding todesirable operation of the compressor, determine flow values of the gasthrough each of the compressor, the fuel cell stack, and the pluralityof pipes based on the detected pressure and the model of the fuel cellcircuit, determine pressure values at each of the compressor, the fuelcell stack, and the plurality of pipes based on the determined flowvalues and the model of the fuel cell circuit, and control operation ofthe compressor based on the control signal, at least one of the flowvalues, and at least one of the pressure values.
 2. The system of claim1 further comprising a flow sensor configured to detect a detected flowvalue of the gas flowing through a second location of the fuel cellcircuit, wherein the ECU is configured to determine the flow values ofthe gas through each of the compressor, the fuel cell stack, and theplurality of pipes further based on the detected flow value.
 3. Thesystem of claim 2 wherein: the detected flow value of the gas is adetected mass flow; the ECU is configured to determine the flow valuesof the gas by determining mass flow values of the gas through each ofthe compressor, the fuel cell stack, and the plurality of pipes and thendetermine laminar, turbulent, or mixed flow values of the gas based onthe mass flow values; and the ECU is configured to determine thepressure values based on the laminar, turbulent, or mixed flow values.4. The system of claim 4 wherein the ECU is further configured to:determine a current output level of the fuel cell stack; determine amolar fraction of the gas output by the fuel cell stack based on thecurrent output level of the fuel cell stack and a quantity of fuel cellsof the plurality of fuel cells; determine a viscosity of the gas outputby the fuel cell stack based on the molar fraction; and furtherdetermine at least one of the laminar, turbulent, or mixed flow valuesof the gas based on the viscosity of the gas output by the fuel cellstack.
 5. The system of claim 1 further comprising: a bypass branchconfigured to cause at least some of the gas to bypass the fuel cellstack; and a bypass valve having a bypass valve position and configuredto adjust an amount of the gas that bypasses the fuel cell stack,wherein the ECU is further configured to determine a current bypass flowvalue corresponding to flow through the bypass branch based on thebypass valve position and a previous bypass pressure value correspondingto the bypass branch and calculated during a previous timestep.
 6. Thesystem of claim 5 wherein the ECU is further configured to determine astack flow value corresponding to flow through the fuel cell stack bysubtracting the current bypass flow value from a total flow valuecorresponding to a total flow of the gas through the fuel cell circuit.7. The system of claim 1 wherein the ECU is further configured toimplement a rate limiter configured to limit a rate of change of atleast one of the pressure values or at least one of the flow values inorder to account for dynamic compressibility of the gas.
 8. The systemof claim 1 wherein the ECU is configured to determine the flow valuesand to determine the pressure values for each component of the fuel cellcircuit during each timestep of operation of the fuel cell circuit.
 9. Asystem for providing oxygen to a fuel cell circuit, comprising: a fuelcell stack having a plurality of fuel cells and configured to receive agas; a bypass branch configured to cause at least some of the gas tobypass the fuel cell stack; a bypass valve having a bypass valveposition and configured to adjust an amount of the gas that bypasses thefuel cell stack; a flow sensor configured to detect a detected flow ofthe gas flowing through a first location of the fuel cell circuit; amemory configured to store a model of the fuel cell circuit; and anelectronic control unit (ECU) coupled to the bypass valve, the flowsensor, and the memory, and configured to: determine or receive acontrol signal corresponding to desirable operation of the bypass valve,determine flow values of the gas through each of the bypass branch andthe fuel cell stack based on the detected flow and the model of the fuelcell circuit, the flow values including a current bypass flow valuecorresponding to flow through the bypass branch, the current bypass flowvalue being determined based on the bypass valve position and a previousbypass pressure value corresponding to the bypass branch that wasdetermined during a previous timestep, determine pressure values at eachof the bypass branch and the fuel cell stack based on the determinedflow values and the model of the fuel cell circuit, and controloperation of the bypass valve based on the control signal, at least oneof the flow values, and at least one of the pressure values.
 10. Thesystem of claim 9 wherein: the detected flow of the gas is a detectedmass flow; the ECU is configured to determine the flow values of the gasby determining mass flow values of the gas through each of the bypassvalve and the fuel cell stack and then determine laminar, turbulent, ormixed flow values of the gas based on the mass flow values; and the ECUis configured to determine the pressure values based on the laminar,turbulent, or mixed flow values.
 11. The system of claim 10 wherein theECU is further configured to: determine a current output level of thefuel cell stack; determine a molar fraction of the gas output by thefuel cell stack based on the current output level of the fuel cell stackand a quantity of fuel cells of the plurality of fuel cells; determine aviscosity of the gas output by the fuel cell stack based on the molarfraction; and further determine at least one of the laminar, turbulent,or mixed flow values of the gas based on the viscosity of the gas outputby the fuel cell stack.
 12. The system of claim 9 further comprising apressure sensor configured to detect a detected pressure of the gasflowing through a second location of the fuel cell circuit, wherein theECU is configured to determine the flow values of the gas through eachof the bypass valve and the fuel cell stack further based on thedetected pressure of the gas.
 13. The system of claim 9 wherein the ECUis further configured to implement a rate limiter configured to limit arate of change of at least one of the pressure values or at least one ofthe flow values in order to account for dynamic compressibility of thegas.
 14. The system of claim 9 wherein the ECU is configured todetermine the flow values and to determine the pressure values for eachcomponent of the fuel cell circuit during each timestep of operation ofthe fuel cell circuit.
 15. A method for providing oxygen to fuel cellscomprising: storing, in a memory, a model of a fuel cell circuit havingmultiple components including a compressor and a fuel cell stack;receiving, from a flow sensor, a detected mass flow of a gas flowingthrough a first location of the fuel cell circuit; determining, by theECU, mass flow values corresponding to mass flow of the gas through eachof the multiple components of the fuel cell circuit; determining, by theECU, a Reynolds number for each of the multiple components based on themass flow values; determining, by the ECU, whether flow of the gasthrough each of the multiple components of the fuel cell circuit is alaminar flow, a turbulent flow, or a mixed flow based on the Reynoldsnumber; determining, by the ECU, laminar, turbulent, or mixed flowvalues of the gas based on the mass flow values and whether the flow ofthe gas through each of the multiple components is the laminar flow, theturbulent flow, or the mixed flow; determining, by the ECU, pressurevalues for each of the multiple components of the fuel cell circuitbased on the laminar, turbulent, or mixed flow values; and controlling,by the ECU, operation of the compressor based on at least one of thelaminar, turbulent, or mixed flow values and at least one of thepressure values.
 16. The method of claim 15 further comprisingreceiving, from a pressure sensor, a detected pressure of the gasflowing at a second location of the fuel cell circuit, whereindetermining the pressure values is further based on the detectedpressure of the gas at the second location.
 17. The method of claim 15wherein determining the mass flow values includes determining a currentbypass mass flow value corresponding to mass flow of the gas through abypass branch that causes at least some of the gas to bypass the fuelcell stack of the fuel cell circuit based on a bypass valve position ofa bypass valve and a previous bypass pressure value corresponding to thebypass branch and calculated during a previous timestep.
 18. The methodof claim 15 further comprising implementing, by the ECU, a rate limiterto limit a rate of change of at least one of the pressure values or atleast one of the mass flow values in order to account for dynamiccompressibility of the gas.
 19. The method of claim 15 furthercomprising: determining, by the ECU, a current output level of the fuelcell stack; and determining, by the ECU, a molar fraction of the gasoutput by the fuel cell stack based on the current output level of thefuel cell stack and a quantity of fuel cells of the plurality of fuelcells; determining, by the ECU, a viscosity of the gas output by thefuel cell stack based on the molar fraction; and further determining, bythe ECU, at least one of the laminar, turbulent, or mixed flow values ofthe gas based on the viscosity of the gas output by the fuel cell stack.20. The method of claim 15 wherein determining the laminar, turbulent,or mixed flow values and determining the pressure values is performed ateach timestep of operation of the fuel cell circuit.